The state-of-the-art is the result of Schulman and Langberg [1]} who suggested a coreset of size \(O(d^2k^3/\varepsilon ^2)\)  for \(k\) -means in the Euclidean case based on non-uniform sampling. The distribution is similar to the distribution in [2]} over the input points, however in [2]} the goal was to have weaker version coresets that can be used to solve the optimal solution, but are of size independent of \(d\) .
